As long as he remained popular, Louis XVI could have have turned the tables if he had had the guts instead of being spineless.
As young Napoleon said : a good shooting would have avoided all this terrible mess. And he knew what he talked about. That's what he did a few years later, in 1795, and that propelled his career to the top.
Unfortunately, Louis' way of thinking was too mechanical for this. He reasoned that Charles I had lost his head BECAUSE he waged war on his people, so IF I don't, I'm safe. So, while a good whiff of grapeshot would've severely simplified matters, it would require Louis to undergo a drastic character change.
I will say, the idea of Louis avoiding his overthrow by having troops fire at unruly citizens hadn't occurred to me -- but that would be, in no small measure, because I don't think that was really much of an option by 1792, when the troops with greater loyalty to the National Assembly and the Revolution were effectively the forces keeping peace in Paris and the armed forces of France.
For that matter, as I was reading up on the Revolution recently, there were no points where I think one might reasonably suppose "
if the forces loyal to the king [assuming there were such forces] had only shot into the mob or opposing force of French, this escalation of the Revolution could have been avoided", much less ended the revolution altogether; maybe, maybe you could make the case that this would have worked in 1789, when it was just the Estates General or the king was still at Versailles, but even if that's the case, it's neither here nor there concerning the OP.
As to Napoleon's part in putting down a royalist uprising in 1795, that was part and parcel of a larger failed effort by the royalists (including the defeat of an invasion months earlier); it did get the Corsican noticed by the government, which is how he got the command in Italy, but that was only the first step in a rise to power with subsequent steps that were... well, contingent to say the least.